Simplify the expression.
$\tan^2\theta-\sec^2\theta+1$

• A. 0
• B. 1
• C. $\csc^2\theta+1$
• D. 2

Answer: (A)

Verified step by step guidance

1. Recognize the trigonometric identity: \( \sec^2\theta = 1 + \tan^2\theta \). This identity will help simplify the expression.
2. Substitute \( \sec^2\theta \) in the expression \( \tan^2\theta - \sec^2\theta + 1 \) with \( 1 + \tan^2\theta \). The expression becomes \( \tan^2\theta - (1 + \tan^2\theta) + 1 \).
3. Simplify the expression by distributing the negative sign: \( \tan^2\theta - 1 - \tan^2\theta + 1 \).
4. Combine like terms: \( \tan^2\theta - \tan^2\theta \) cancels out, and \( -1 + 1 \) also cancels out, leaving \( 0 \).
5. Conclude that the simplified expression is \( 0 \).